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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '113246208.d', 'ambient_counter': 4, 'ambient_order': 113246208, 'ambient_tex': 'C_2^{12}.S_4^3:C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 28311552, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '113246208.d.4._.BG', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.BG', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28311552.ci', 'subgroup_hash': None, 'subgroup_order': 28311552, 'subgroup_tex': 'C_2^{10}.(A_4\\times S_4^2):C_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '113246208.d', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6227020801, 356995102464126, 8683317618811886495518194407507383681, 10341831284004956842014307915909865839920, 25903107681056726359680, 25852016738885016556800, 5041, 25852016738884976645040, 51212944267221104046, 8691540457481899984538088985995171246, 10904380660461683146752000007, 121, 367920, 127648036701462510001505284712137188235440, 126, 52855354610938228238220904188053995912296, 8691540457466090321443601020886001840, 15511210043330985984000001, 228643658167481876546209646127486, 8841777505000958228495373756720, 116697269768863977230721345184098191252992, 8691540457481601480400525976744639286, 1313901388807], 'label': '113246208.d.4._.BG', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '4.BG', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4._.BG', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[63841915533051527541432038788198329613849, 276570711494917108631857392691983377126704], [74183738603048718869393447449394457716537, 276570711485397720193474323644628214656311], [74175055084010923414695376935766326927377, 127656720046238984445586768721219777777406], [63841915533051527541432038788198329613849, 276570711494917108631857392691983377126704], [191498618850067043386831264691650715942422, 286903867674622519301063792707714295024231], [85080784139235806185388756472436380954839, 276579403035363670341416192368518950230631], [74175055285429891417413943060889625256014, 276570711503758855114387050959847354010030], [74183746825898261836691814865973408946775, 276570711494906204251196931007522723738025], [63850590627820811865861256556106746434848, 276579403035363670341416192724200191217705], [74183746825898261836691814865973408946775, 286903867684141907739395649167797339222624], [191489935532448231500335746497249475859222, 276570711503758870625597094645213091738031], [63850598740774851205902588344885457945022, 159255831046468911461009677629683489416031], [63850598850670354913234492633830354518168, 276579403044216321178805387234191308017591], [63850598850670354913285461573906553030095, 276570711494906204251196931008830398105905], [63841915533051527515528931108443130434848, 276570711503758855114387051314227107737911], [74175063508279434438986253340586144941729, 276570711494917108631857392334982047642031], [63850598850670354913234492633830354518168, 276570711494917108631857392334982047642031], [63850590627820811891764364235861985167648, 276570711503747981756146675938672570010025], [63841915533051527515580022049307165869729, 276570711503758870625597094646520766106030], [74183738594217845664978326245790674886088, 276579403044216321204606312676531008230824], [63841915533040654157288556087268346434969, 276579403044205447846416906952421298185945], [63850598850670354913234492633830354518168, 286903867684131003358786399714927603030750], [63841915541882400639869183650902176946768, 286912542787763811956350146642864855305831], [63841915541893289535120527801090073256008, 276579394812535905032994762647875566571865], [74175055285440795772222510004631603455575, 276579403035374574722076654052967149210030], [201823083507676153960753069272709158627142, 276570711476555942714376473452883222743991], [201831775039302746875029982851925331427263, 286903867674622519301063792707714295024231], [201831775039302746875081195439197449699256, 255304748579821480573888947189123435862446], [201823083498834376455854292928557203750536, 265629204996897493064788189555476388843560], [201831766825294950336038422491017858691136, 265629213219736162753920929322612272102526]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 2038431744, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 3, 2], [2, 6, 1, 4], [2, 9, 1, 2], [2, 12, 1, 2], [2, 18, 1, 4], [2, 18, 2, 2], [2, 18, 3, 2], [2, 18, 6, 4], [2, 18, 9, 4], [2, 27, 3, 6], [2, 27, 9, 4], [2, 36, 1, 8], [2, 36, 2, 2], [2, 36, 3, 2], [2, 36, 6, 4], [2, 36, 9, 4], [2, 48, 2, 1], [2, 54, 1, 6], [2, 54, 3, 2], [2, 54, 6, 4], [2, 54, 9, 14], [2, 54, 18, 4], [2, 108, 1, 8], [2, 108, 2, 2], [2, 108, 3, 16], [2, 108, 6, 8], [2, 108, 9, 20], [2, 108, 18, 16], [2, 144, 2, 1], [2, 144, 4, 1], [2, 144, 6, 1], [2, 216, 1, 6], [2, 216, 3, 2], [2, 216, 6, 4], [2, 216, 9, 14], [2, 216, 18, 4], [2, 288, 2, 1], [2, 432, 2, 2], [2, 432, 4, 1], [2, 432, 6, 1], [2, 432, 12, 2], [2, 432, 18, 2], [2, 576, 1, 2], [2, 864, 2, 2], [2, 864, 4, 1], [2, 864, 6, 1], [2, 864, 12, 2], [2, 864, 18, 2], [2, 1728, 3, 2], [2, 3456, 1, 2], [3, 256, 1, 1], [3, 8192, 1, 1], [3, 16384, 1, 1], [3, 16384, 2, 1], [3, 32768, 1, 1], [4, 48, 2, 1], [4, 144, 2, 3], [4, 144, 4, 1], [4, 144, 6, 1], [4, 144, 12, 2], [4, 144, 18, 2], [4, 288, 2, 1], [4, 432, 2, 4], [4, 432, 4, 1], [4, 432, 6, 5], [4, 432, 12, 4], [4, 432, 18, 8], [4, 432, 36, 8], [4, 576, 1, 2], [4, 864, 2, 4], [4, 864, 4, 1], [4, 864, 6, 5], [4, 864, 12, 4], [4, 864, 18, 8], [4, 864, 36, 8], [4, 1152, 1, 2], [4, 1728, 3, 6], [4, 1728, 9, 4], [4, 3456, 1, 10], [4, 3456, 2, 2], [4, 3456, 3, 4], [4, 3456, 6, 8], [4, 3456, 9, 18], [4, 3456, 18, 4], [4, 4608, 2, 1], [4, 4608, 6, 1], [4, 13824, 2, 1], [4, 13824, 6, 3], [4, 13824, 18, 2], [4, 27648, 2, 1], [4, 27648, 6, 3], [4, 27648, 18, 2], [4, 110592, 2, 1], [4, 110592, 6, 1], [6, 256, 1, 1], [6, 768, 1, 2], [6, 768, 2, 2], [6, 768, 3, 2], [6, 1536, 1, 2], [6, 2304, 1, 4], [6, 2304, 2, 2], [6, 2304, 3, 2], [6, 2304, 6, 4], [6, 2304, 9, 4], [6, 4608, 1, 4], [6, 4608, 2, 2], [6, 4608, 3, 2], [6, 4608, 6, 4], [6, 4608, 9, 4], [6, 6144, 2, 1], [6, 8192, 1, 1], [6, 16384, 1, 1], [6, 16384, 2, 1], [6, 18432, 4, 1], [6, 18432, 6, 1], [6, 24576, 2, 2], [6, 32768, 1, 1], [6, 49152, 2, 4], [6, 49152, 3, 2], [6, 49152, 4, 1], [6, 73728, 1, 2], [6, 98304, 1, 2], [6, 98304, 2, 2], [6, 98304, 4, 1], [6, 147456, 2, 2], [6, 147456, 4, 1], [6, 294912, 1, 4], [6, 294912, 4, 1], [8, 110592, 2, 1], [8, 110592, 6, 3], [8, 110592, 18, 2], [12, 6144, 2, 1], [12, 18432, 2, 2], [12, 18432, 4, 1], [12, 18432, 6, 1], [12, 18432, 12, 2], [12, 18432, 18, 2], [12, 49152, 4, 1], [12, 98304, 4, 1], [12, 147456, 4, 1], [12, 294912, 1, 2], [12, 294912, 2, 2], [12, 294912, 4, 1], [12, 589824, 2, 1], [12, 589824, 6, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 6], [2, 6, 4], [2, 9, 2], [2, 12, 2], [2, 18, 74], [2, 27, 54], [2, 36, 78], [2, 48, 2], [2, 54, 234], [2, 108, 576], [2, 144, 12], [2, 216, 234], [2, 288, 2], [2, 432, 74], [2, 576, 2], [2, 864, 74], [2, 1728, 6], [2, 3456, 2], [3, 256, 1], [3, 8192, 1], [3, 16384, 3], [3, 32768, 1], [4, 48, 2], [4, 144, 76], [4, 288, 2], [4, 432, 522], [4, 576, 2], [4, 864, 522], [4, 1152, 2], [4, 1728, 54], [4, 3456, 308], [4, 4608, 8], [4, 13824, 56], [4, 27648, 56], [4, 110592, 8], [6, 256, 1], [6, 768, 12], [6, 1536, 2], [6, 2304, 74], [6, 4608, 74], [6, 6144, 2], [6, 8192, 1], [6, 16384, 3], [6, 18432, 10], [6, 24576, 4], [6, 32768, 1], [6, 49152, 18], [6, 73728, 2], [6, 98304, 10], [6, 147456, 8], [6, 294912, 8], [8, 110592, 56], [12, 6144, 2], [12, 18432, 74], [12, 49152, 4], [12, 98304, 4], [12, 147456, 4], [12, 294912, 10], [12, 589824, 8]], 'center_label': '2.1', 'center_order': 2, 'central_product': None, 'central_quotient': '14155776.ee', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 23, 'conjugacy_classes_known': False, 'counter': 61, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 6], [2, 6, 1, 4], [2, 9, 1, 2], [2, 12, 1, 2], [2, 18, 1, 74], [2, 27, 1, 54], [2, 36, 1, 78], [2, 48, 1, 2], [2, 54, 1, 234], [2, 108, 1, 576], [2, 144, 1, 12], [2, 216, 1, 234], [2, 288, 1, 2], [2, 432, 1, 74], [2, 576, 1, 2], [2, 864, 1, 74], [2, 1728, 1, 6], [2, 3456, 1, 2], [3, 256, 1, 1], [3, 8192, 1, 1], [3, 16384, 1, 1], [3, 16384, 2, 1], [3, 32768, 1, 1], [4, 48, 1, 2], [4, 144, 1, 76], [4, 288, 1, 2], [4, 432, 1, 522], [4, 576, 1, 2], [4, 864, 1, 522], [4, 1152, 1, 2], [4, 1728, 1, 54], [4, 3456, 1, 308], [4, 4608, 2, 4], [4, 13824, 2, 28], [4, 27648, 2, 28], [4, 110592, 2, 4], [6, 256, 1, 1], [6, 768, 1, 12], [6, 1536, 1, 2], [6, 2304, 1, 74], [6, 4608, 1, 74], [6, 6144, 1, 2], [6, 8192, 1, 1], [6, 16384, 1, 1], [6, 16384, 2, 1], [6, 18432, 1, 10], [6, 24576, 2, 2], [6, 32768, 1, 1], [6, 49152, 1, 6], [6, 49152, 2, 6], [6, 73728, 1, 2], [6, 98304, 1, 2], [6, 98304, 2, 4], [6, 147456, 2, 4], [6, 294912, 1, 4], [6, 294912, 2, 2], [8, 110592, 2, 28], [12, 6144, 1, 2], [12, 18432, 1, 74], [12, 49152, 2, 2], [12, 98304, 2, 2], [12, 147456, 2, 2], [12, 294912, 1, 2], [12, 294912, 2, 4], [12, 589824, 2, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 24, 'exponents_of_order': [20, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': None, 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '14155776.ee', 'hash': 4671628737574694319, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 14155776, 'inner_split': None, 'inner_tex': 'C_2^{12}.S_4^2:S_3', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '28311552.ci', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C2^10.(A4*S4^2):C4', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 0, 3, 0, 3, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 3, 0, 1, 0, 3, 1, 0, 0, 1, 3, 0, 0, 1, 6, 1, 0, 0, 10, 1, 0, 0, 10, 0, 0, 0, 6, 0, 1, 3, 0, 3, 1, 3, 0, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 464, 'number_characteristic_subgroups': 41, 'number_conjugacy_classes': 3456, 'number_divisions': 3330, 'number_normal_subgroups': 95, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 28311552, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 247807], [3, 90368], [4, 5093376], [6, 6463232], [8, 6193152], [12, 10223616]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '144.192', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 144, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'D_6^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '16413850406164961890679989708263021646880728003126437466800911219475546793435002849452547487910297889586496534489613151743494032258128348538846264803556182666168112352008608570914721435152932014515111289670275907683908809225625866299784903689843579144869392725153530158570556011273318047198033624814893184703662605256322468631277111581651307158750393752399192791309683271655767731527024014707391139731319963645143494348051187424048654156106079682117252056304677409630484340019063837261730295250764639816824639360242417081321853454411229537745741775543202955837914778268919893514337697406619890443115601019961436182965658131915908319848190079267174779273366711632009491550282492780954889364227368078767979341882764132094227181697360969362766201436903551646938707443147103406221691204044455082723702786076599580807836728195429832690350562334705280886623044530475927134771479293473361094324888006514145009728155884064982714978285484157762460697809993104314380071872462142358303922007593865566315221761654964062228713393638228492564073576350953747058345224918965309554688', 'gens': [1, 3, 5, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], 'pres': [23, 2, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 46, 163745304, 1846691438, 30716479, 186, 2016373571, 547791946, 4302360, 2546936284, 427702047, 658708550, 132025018, 326, 3296605829, 16281820, 1940883, 5724038, 3830126250, 2185706405, 472124824, 254373474, 2783144, 977230, 3462288, 3144077191, 1199447454, 47083445, 535139788, 164390115, 796106, 3958721, 536, 83005352, 2243588575, 91629846, 206047877, 61051852, 8904458, 6370979769, 931798112, 237275875, 187867068, 3204461, 538324, 23319387, 7420430, 8302963, 4342767274, 122848737, 1100774720, 541097251, 1056630, 1184165, 5446732, 1169031, 2139056, 6572326187, 756407842, 1446766113, 131276996, 2146279, 283302, 5517964, 2547123, 4232577036, 4133411, 12400186, 9300177, 516776, 172351, 6837239821, 2225700, 14536427, 11128402, 185577, 278336, 9157017614, 16692517, 14382420, 14307923, 4173226, 1689249, 10093068303, 27979814, 38233789, 17169492, 5100587, 1702498, 8475328528, 56754471, 19002662, 14230921, 1576620, 2590115, 114462737, 1190412328, 274710591, 732561494, 7631026, 4133577, 72493074, 2319777856, 289972311, 5370012, 2685107, 2013898, 6756499, 610467882, 813957185, 330670168, 2826397, 4239540, 706763, 47156276, 1068318763, 1068318786, 774531161, 22256798, 8160949, 1113036, 20984853, 727474243, 55959642, 74612895, 37306550, 12435661, 14625814, 5616304173, 58503236, 175509595, 13000887, 19501262]}, 'Perm': {'d': 36, 'gens': [276570711494917108631857392691983377126704, 63841915533051527541432038788198329613849]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 27, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_2^{10}.(A_4\\times S_4^2):C_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.14', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[159237946280793871936931927451214857811489, 170170234903374042958445638098692528446776, 276579394830840916295079291146567305825505, 116697269768863977230721345184098191252992], [159237946280793871936931927451214857811489, 170170234903374042958445638098692528446776, 276579394830840916295079291146567305825505, 106355430270851254846334637775154823105359], [180521275821641999618509082235138594912719, 148922691147552288735830786306680871141471, 297809588397113228458687178783615546990136, 85089459133560303743666034683061857773735], [159237946390678471289506350049079453626008, 170170234903374042958445638455687630910662, 276579394775904037867791226607885232562145, 106355430270851254547830738967512480895879], [170188127965151373959139374894111722986232, 286912551028918351053101759536043155985705, 170161559863552510043382729337675211291383, 223070643700344327417129205793113356898854], [286885966591515920312895462263165624357448, 308151411293436291251602238150830011473862, 159255839168886169939866796364620060356785, 361651487164320325209826600085651216639992], [159237946280793871936931927451214857811489, 170170234903374042958445638098692528446776, 276579394830840916295079291146567305825505, 116697269768863977230721345184098191252992], [180521275821641999644361220619123940472838, 170161559808593885224021042536069560638783, 276579394839682662777608949770124938183350, 63841915395411200176193076168517069895056], [159237946271941221073741807498890227539615, 170170234894543169834156354853304782910662, 276579394839682662777608949414431282708824, 106355438484848147030517874835587067846279], [159237946280793871936931927451214857811489, 170170234894532265453495893168844129521857, 276579394830851789653319666166428188436710, 116688578237237384290643262520583282682958], [159237946280793871936931927451214857811489, 180503391092598842040183212067994000727016, 276570719736060758586455621380657605575345, 106355438484848147030517874835587067846279], [148913481632026538919663901989149584337569, 180494699552141375975713663560757722087096, 286912551020065715376816865115868778095665, 116688578237237384290643262520583282682958], [159237946271941205562531764169211917907494, 170170234958332668102214446229885452709063, 276579394674839407421023644701612883250270, 371993318558209896889773232923975558725758], [159246621375574029645555840507325376083489, 180494699552141376001565680299642699089976, 286903859479608249338250424289689186271585, 244336614984816787764181758390250232948993], [159237946280782983067481509454747744928414, 170170234894543169834156354496309680446662, 276579394839693551647059368120971804436825, 106355438484848147056369891573164369755398], [148904790091569072829342458388128737899729, 170170234903374042958445638098692528446776, 276579394830840916295079291146567305825505, 106355438493700797893656782910713028602839], [159237946280793871936931927805600838560414, 170170234903374042958445638455681403889863, 276579394839693551647059368122285705825630, 106355430270851254872135685216968499137232], [148904790091569072855194596772114163283489, 170170234903374042958445638098692528446776, 276579394830840916295079291146567305825505, 116688578228395637782261708801927141206478], [159246621375574029671356766304038603729569, 170161559808593885224021042536069520359096, 286912551020065715376765652528596700103345, 116688578228406511166303009621129134074958], [159237946271941205562531763813524489811614, 170170234903374042958445638098692528446776, 276579394839693551647059368122285705825630, 116697269768863977204920298099273351105359], [159237946271952094431982182520071238560295, 170170234894532265453495893170151803889982, 276579394839693551647059367765290603361504, 106364121802477847786463811382155382783879], [159237946271952109943192225851050995539495, 170170234903374042958445638099993975793983, 276579394839682678288818992744115819361511, 116697269768863977230772436127577575423878], [159237946280793856425721884120228873811488, 170170234903374042958445638454373729521857, 276579394830851805164529709497414172436704, 116697269768863977204869328445206947675393], [148904798305555076169978385131836694723529, 180503382869771061246301573516526437095097, 286912551020076604272119299849919420276825, 116688578237248273160093680515748947861112], [148904790091569072855245566069185464259409, 180503391092598842040131999480721922008936, 286903859479608249338199454992617885295665, 116697269777694850355061598440547442682832], [159237938057955217759009109725651977816529, 180503382869760187862260394342431160643816, 276570711513222104408583894597266435015345, 116697269777705739224460925849228826511952], [286894658131984290758025472454862556376095, 308142736198667006901218943404781193119217, 159264514263655454290148152516526276779750, 371993318457156155176181160546635436712198], [308169312569221387606740642454876287538552, 286912542632383790356950593730206446942385, 170170234958332668076311460193929175103216, 340376832727083228386963567758248014399574], [297836164611677004696665710166469068357632, 286903867537614537028987385646142050629350, 180503382915877051038090425960106267730536, 350709988907466249963751153507500270081055], [308160621028753048184030718927766672971599, 276579394674839407395171627964029354315305, 170161559863541637009549354002288739416263, 350709988907466249963751153507500270081055], [170179452870382089608858262032418777543119, 286903859479619122994994933893120069803745, 180494707829927781640661022394210091195376, 212737487511130417153138016699510373716688]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 1811939328, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': None, 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 3, 2], [2, 6, 11], [2, 9, 2], [2, 12, 5], [2, 18, 45], [2, 27, 10], [2, 36, 102], [2, 48, 4], [2, 54, 91], [2, 72, 53], [2, 108, 363], [2, 144, 16], [2, 192, 2], [2, 216, 543], [2, 288, 8], [2, 384, 1], [2, 432, 257], [2, 576, 2], [2, 864, 96], [2, 1152, 5], [2, 1728, 56], [2, 2304, 4], [2, 3072, 1], [2, 3456, 8], [2, 6912, 7], [2, 9216, 1], [2, 13824, 1], [3, 256, 1], [3, 8192, 1], [3, 16384, 1], [3, 32768, 2], [4, 48, 4], [4, 144, 48], [4, 192, 2], [4, 288, 56], [4, 384, 5], [4, 432, 140], [4, 576, 2], [4, 864, 592], [4, 1152, 49], [4, 1728, 472], [4, 2304, 76], [4, 3072, 1], [4, 3456, 200], [4, 4608, 32], [4, 6912, 519], [4, 9216, 7], [4, 13824, 285], [4, 18432, 4], [4, 27648, 190], [4, 55296, 76], [4, 73728, 2], [4, 110592, 26], [4, 221184, 6], [4, 442368, 2], [6, 256, 3], [6, 768, 16], [6, 1536, 8], [6, 2304, 44], [6, 4608, 96], [6, 6144, 4], [6, 8192, 1], [6, 9216, 52], [6, 12288, 4], [6, 16384, 2], [6, 18432, 12], [6, 32768, 5], [6, 36864, 8], [6, 49152, 6], [6, 65536, 1], [6, 73728, 6], [6, 98304, 19], [6, 147456, 1], [6, 196608, 11], [6, 294912, 12], [6, 393216, 3], [6, 589824, 6], [6, 786432, 1], [6, 1179648, 1], [8, 73728, 2], [8, 221184, 22], [8, 442368, 26], [12, 6144, 4], [12, 12288, 12], [12, 18432, 44], [12, 36864, 96], [12, 73728, 76], [12, 98304, 4], [12, 147456, 32], [12, 196608, 6], [12, 294912, 6], [12, 393216, 7], [12, 589824, 9], [12, 786432, 1], [12, 1179648, 7], [12, 2359296, 6], [24, 2359296, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': None, 'central_quotient': '56623104.bg', 'commutator_count': None, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 25, 'conjugacy_classes_known': False, 'counter': 4, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 3, 1, 2], [2, 6, 1, 11], [2, 9, 1, 2], [2, 12, 1, 5], [2, 18, 1, 45], [2, 27, 1, 10], [2, 36, 1, 102], [2, 48, 1, 4], [2, 54, 1, 91], [2, 72, 1, 53], [2, 108, 1, 363], [2, 144, 1, 16], [2, 192, 1, 2], [2, 216, 1, 543], [2, 288, 1, 8], [2, 384, 1, 1], [2, 432, 1, 257], [2, 576, 1, 2], [2, 864, 1, 96], [2, 1152, 1, 5], [2, 1728, 1, 56], [2, 2304, 1, 4], [2, 3072, 1, 1], [2, 3456, 1, 8], [2, 6912, 1, 7], [2, 9216, 1, 1], [2, 13824, 1, 1], [3, 256, 1, 1], [3, 8192, 1, 1], [3, 16384, 1, 1], [3, 32768, 1, 2], [4, 48, 1, 4], [4, 144, 1, 48], [4, 192, 1, 2], [4, 288, 1, 56], [4, 384, 1, 5], [4, 432, 1, 140], [4, 576, 1, 2], [4, 864, 1, 592], [4, 1152, 1, 49], [4, 1728, 1, 472], [4, 2304, 1, 76], [4, 3072, 1, 1], [4, 3456, 1, 200], [4, 4608, 1, 32], [4, 6912, 1, 519], [4, 9216, 1, 7], [4, 13824, 1, 285], [4, 18432, 1, 4], [4, 27648, 1, 190], [4, 55296, 1, 76], [4, 73728, 1, 2], [4, 110592, 1, 26], [4, 221184, 1, 6], [4, 442368, 1, 2], [6, 256, 1, 3], [6, 768, 1, 16], [6, 1536, 1, 8], [6, 2304, 1, 44], [6, 4608, 1, 96], [6, 6144, 1, 4], [6, 8192, 1, 1], [6, 9216, 1, 52], [6, 12288, 1, 4], [6, 16384, 1, 2], [6, 18432, 1, 12], [6, 32768, 1, 5], [6, 36864, 1, 8], [6, 49152, 1, 6], [6, 65536, 1, 1], [6, 73728, 1, 6], [6, 98304, 1, 19], [6, 147456, 1, 1], [6, 196608, 1, 11], [6, 294912, 1, 12], [6, 393216, 1, 3], [6, 589824, 1, 6], [6, 786432, 1, 1], [6, 1179648, 1, 1], [8, 73728, 1, 2], [8, 221184, 1, 22], [8, 442368, 1, 26], [12, 6144, 1, 4], [12, 12288, 1, 12], [12, 18432, 1, 44], [12, 36864, 1, 96], [12, 73728, 1, 76], [12, 98304, 1, 4], [12, 147456, 1, 32], [12, 196608, 1, 6], [12, 294912, 1, 6], [12, 393216, 1, 7], [12, 589824, 1, 9], [12, 786432, 1, 1], [12, 1179648, 1, 7], [12, 2359296, 1, 6], [24, 2359296, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 24, 'exponents_of_order': [22, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': None, 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '14155776.fs', 'hash': 3194120075579178902, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 56623104, 'inner_split': None, 'inner_tex': 'C_2^{10}.(S_4^3.C_2^2)', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '113246208.d', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C2^12.S4^3:C2', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 0, 2, 0, 1, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 1, 0, 3, 0, 3, 0, 1, 1, 3, 0, 2, 3, 1, 0, 1, 8, 1, 0, 1, 6, 3, 0, 0, 9, 3, 0, 0, 10, 1, 1, 0, 14, 0, 7, 0, 8, 0, 19, 7, 0, 27, 1, 35, 0, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 118, 'number_conjugacy_classes': 5184, 'number_divisions': 5184, 'number_normal_subgroups': 224, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 113246208, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 584703], [3, 90368], [4, 24843264], [6, 17047296], [8, 16515072], [12, 49446912], [24, 4718592]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 32, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '2821597677674657638016045925292905724155285202667084542777020725613649322868321950885411403422677387587753091974511176642589372359095730379440250404172942178971792636095118162277174634131567981936827773788888463939187644208408527280555984531471935787581256446641390582558966077691632428402393890813514716009012788743473957566892653967557750487685738072020361039287415035798594418722837071928785023858667850958460126117956190556396293965441113996689375624752609076578600685506056190714202825410025816977680069926614260489717431760027573541347312205680138437694083832249065246109074826376632252893790081637960343355788597742666773550946090786152531789684762181691836030732019407167283191285938201723730558680671395150877908537852347931779483489156326804694670028145440861596242092610138750377711644767554775431653758007130427795072883738153975346065198012868693443681383351022069756509809791987788882996176969235887446452276551252121167052558035303878067481523246121560265254288544191711796055906215832936958652655700806198151989334288299902750417218613996996133065069081058172426267785508257282965757729747001183032089803878771228488536055833833872703374560098033975878872556309767997970449106304538719120182889225764873536422078062680552929662809304548415323628603932396975996956203503814561585590349722708159377544729442443256153245430404608973122115676186690721089172794934331699522315685417774683200888139485539801510817668405035008', 'gens': [1, 2, 3, 4, 5, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], 'pres': [25, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 165786000, 2017184901, 1285691226, 600474302, 3857169777, 433307452, 9786228003, 5014074028, 787330653, 333870078, 5691358004, 2953321029, 390402554, 1555685829, 354, 14011627205, 4122319230, 4066590055, 766720280, 82944130, 2270822406, 135668431, 2485812056, 941070981, 553110706, 154838906, 506, 17694950407, 55334432, 19257, 43550482, 17630507, 692532, 17627068808, 10805821233, 57591058, 1360824383, 238379058, 22568758, 66615908, 98058, 658, 235104009, 9068688034, 3539016059, 2543652084, 608292109, 483849134, 221187159, 6686143210, 6456582035, 6297112860, 1208859385, 449004710, 677251710, 247660, 282335, 43086660, 14362660, 17302204811, 1064016036, 6902625661, 2920212086, 265842111, 145936, 22122211, 5531636, 25334899212, 11586135637, 8134939862, 4050621987, 1602426262, 589911212, 421362, 163987, 43937612, 2000937, 1857945613, 285465638, 4838463, 48384088, 1209713, 5745738, 1411363, 756188, 31186944014, 77760039, 49248064, 12960089, 12312114, 324139, 1080164, 432189, 28311552015, 210124840, 141004865, 70502490, 35251315, 13132940, 806565, 172990, 4512153616, 5875241, 117504066, 2937691, 29376116, 5508141, 244966, 612191, 43794432017, 373248042, 68428892, 5702567, 3888192, 15969484818, 72230443, 128044868, 21340893, 32011318, 2052143, 7797768, 1710193, 193536019, 20791296044, 3096576069, 221184094, 1492992119, 1133568144, 3072219, 2304244, 14515220, 19043942445, 6270566470, 348364895, 812851320, 174182545, 4838620, 806645, 45619221, 29196288046, 5839257671, 2919628896, 729907321, 243302546, 74342621, 33792246, 270259222, 10174464047, 11191910472, 6613401697, 254361722, 381542547, 91853022, 52992247, 613785623, 3715891298, 3715891323, 1061683348, 58982623, 44237048, 362880024, 7741440099, 1935360124, 1658880149, 92160224, 15360249]}, 'Perm': {'d': 36, 'gens': [116697269768863977230721345184098191252992, 170170234903374042958445638098692528446776, 276579394830840916295079291146567305825505, 159237946280793871936931927451214857811489]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 18, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_2^{12}.S_4^3:C_2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': None}
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 3]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
